Nonlinear norm-observability and simulation of control systems

The (bi)simulation relation has recently been attracting growing interest in the study of nonlinear control systems, in the hope that through such a relation, the behaviors and properties of a nonlinear system can be inferred from those of another system which is easier to handle. In this paper, we consider the propagation of the property of nonlinear norm-observability through a simulation relation. Given two control systems that are related by a graph simulation relation, we derive conditions under which the norm-observability of the simulating system implies the norm-observability of the simulated system. The obtained results are given in terms of set-valued functions. Several examples are included to illustrate various applications of our results.